Are Photons Actually Infinitely Small Particles?

[Cthugha]

Why does a region where the particle is localized have to be its size? Does it mean that the size of the electron is one Bohr radius in the hydrogen atom?

That is a clever way of turning around the question. I am not saying that the region where a particle is localized HAS TO BE its size. I am saying that it can be (and in some subfields it also is) defined as such.

My position is rather: Why does the internal structure of a particle have to determine the size? It is defined that way in relativity where the internal structure is of most interest. It is usually defined and used differently in e.g. quantum chemistry (see e.g. PNAS 106, 1001-1005 (2009) by Su et al.), chemical physics, some branches of semiconductor physics and other areas where the internal structure is not of interest.

Localizability is also more heavily studied in quantum optics where e.g. the energy density and the detection probability are nonlocally connected for polychromatic photons (see Mandel/Wolf, chapter 12.11.5).

I just think it is pointless to argue about semantics here. The "natural" meaning of size differs from discipline to discipline and I do not think that it is disputed that many quantities of interest associated with photons/electrons have some spatial extent. If this was the relativity forum I would agree that one should stick to the internal structure meaning of size. In the QM section, however, in my opinion the situation is quite different.

 

[A. Neumaier]

I have a question on the slides from A. Neumaier:

According to my understanding, in QED electromagnetism is quantized by first identifying a bunch of modes of the classical field - these are solutions of Maxwell's equations, then quantizing by treating the mode expansion coefficients as raising and lowering operators. This way the one-photon state has certain non classical properties etc etc.

This is not quite accurate. The modes simply form a basis of all solutions of the Maxwell equations - arbitrary superpositions of these modes represent arbitrary solutions. All these superpositions are quantized as well. Quantization is therefore independent of how one chooses the modes - different choices give equivalent quantizations.

If I understood correctly, in your proposal this one-photon state can carry "photon particles" which are localized lumps of energy. Does this mean that the energy in the one-photon state (which has total energy \hbar\omega) can be delivered to a detector in lumps smaller than \hbar\omega ?

No. In the situation where a 1-photon state describes a particle, one has only a single lump, and the whole energy is delivered in one piece.

A general 1-photon state can be an arbitrary solution of the Maxwell equation. It deserves to be regarded as a particle if and only if this solution is essentially localized in a single lump (or wave packet). Such 1-photon states are called ''photons on demand''. The lump then moves with the speed of light along the beam. Essentially the full energy of the state is then localized in the lump, and therefore moves to the detector, where it causes a detection event (with a certain probability).

Or does it simply mean that the modes you originally choose to excite to define the one-photon state have these localization properties ?

A photon on demand is prepared in such a lumpy mode.

Have you written more on this issue ?

No. But the slides contain references to the literature on photons on demands.

 

[A. Neumaier]

Wouldn't a point particle by definition be something the size of a Planck length?

No. By definition, a point particle has size 0, which is infinitely many orders of magnitude smaller than the Planck length. A particle of the size of the Planck length is obviously extended.

 

[A. Neumaier]

if you could catch
a photon you would find that it weighed nothing at all.

How do you know?

A photon with energy E has an inertial mass of m=E/c^2, hence would weight something if it could be reliably weighted...

 

[YummyFur]

Hang about, even I know that weight is not mass. Tighten it up a bit fellas.

 

[YummyFur]

No. By definition, a point particle has size 0, which is infinitely many orders of magnitude smaller than the Planck length. A particle of the size of the Planck length is obviously extended.

Yes that makes sense but wouldn't something the size of the Planck length fall underneath the radar of the uncertainty principle? Is it allowable to suggest something smaller than the Planck length.

Also if string theory suggests strings about the Planck size, which are said to be many orders of magnitude smaller than the size of currently referred to point particles like an electron there would appear to be some confusion, at least to the lay public, about what do physicists mean by 'point particle'.

It annoyed me when years ago I would marvel at particles that had mass but no size, naively thinking that physicists would be telling the truth, only to find later that these we're not point particles at all.

Even the aforementioned strings are referred to as point particles while at the same time presenting as objects with length and breadth, I mean by the very definition a string cannot be a point.

 

[Fredrik]

Yes that makes sense but wouldn't something the size of the Planck length fall underneath the radar of the uncertainty principle? Is it allowable to suggest something smaller than the Planck length.

The Planck length is not special in any of the established theories (QM, GR, etc.). These theories all describe things that are smaller, in the same way as the describe things that are much larger. They are however expected to be very wrong about things at small enough distance scales, and a simple order-of-magnitude estimate suggests that the Planck length is "small enough" in this sense.

What do I mean by "a simple order-of-magnitude estimate"? I mean something like estimating the volume of a sphere to be r³ where r is the radius, because the volume clearly depends on the radius, and r³ has the right units. This estimate is wrong by a factor of about 4. This is of course to be expected since the method ignores almost all the details. But experience tells us that these crude estimates are rarely wrong by many orders of magnitude.

Also if string theory suggests strings about the Planck size, which are said to be many orders of magnitude smaller than the size of currently referred to point particles like an electron there would appear to be some confusion, at least to the lay public, about what do physicists mean by 'point particle'.

In a classical theory with spacetime M, a point particle can be defined as a pair (x,m) where x:(a,b)→M is a function that satisfies an equation of the form mx''(t)=F(x'(t),x(t),t). The number m is of course called the "mass" of the particle. Point particles in quantum theories are much harder to define. Non-interacting particles can be defined in terms of irreducible representations of groups, but I don't know if there even is a good definition of interacting point particles in 3+1-dimensional spacetime.

 

[technician]

The best and only answer I give to my students is : photons are emitted in less than 10^-10secs.perhaps it is 10^-9 secs.
They travel at the speed of light... 3 x 10^8 m/s
therefore photons have a length of the order 0.3m...
go and join in the many discussions about the size of photons

 

[A. Neumaier]

It annoyed me when years ago I would marvel at particles that had mass but no size, naively thinking that physicists would be telling the truth, only to find later that these we're not point particles at all.

Well, there are levels of rigor in talk. For the laymen, one has to take all concepts with a large grain of salt, in order to be able to communicate at least a bit. With more specialized education, one can be more and more precise about what things really mean. If one would be allowed to say only things that are rigorously true, almost nobody would understand it...

 

[A. Neumaier]

Hang about, even I know that weight is not mass. Tighten it up a bit fellas.

An object that has a nonzero mass will have a nonzero weight when put on a scale in a nonzero gravitational field: F=mg. How much it weighs depends on the strength g of the graviitation. Thus weight is not mass, but from the existence of a nonzero mass one can conclude the existence of a nonzero weight.

Moreover, by general relativity, it is not the rest mass that counts here (which for photons is zero) but the mass equivalent of the total energy (which for photons in nonzero, E = hbar*omega).

So if one had a scale with a resolution high enough to detect the difference of the presence and the absence of a photon, it could be weighted.

 

[fizzle]

BUT, what about when we are dealing with low Radio Frequency em? Consider a photon with an 'extent' of just one wavelength. For a 200kHz transmission, that represents a wavelength of 1500m. Now take a very simple transmitter with, say, the collector of a transistor connected to a short wire. Take an equally simple receiver, with a short wire connected to the base of transistor. Separate them by 10m. The receiver will receive photons that the transmitter is sending it. These photons, if they were to have the proposed extent would have to extend from the transmitter to a region that is 100 times as far away as the receiver input or, they would somehow need to extend ('coiled up?' somehow) from within the transmitter to somewhere within the nearby receiver. This just has to be a nonsense model. In fact you just can't allow a photon to have any extent al all or there will be some circumstance like the above that spoils the model.

If I understand the whole "photon" business correctly, a radio wave would be composed of waves of billions of photons (one for each electron excited in the antenna), not a single "photon" at 200 kHz. The number of photons would be proportional to the magnitude of the radio wave and that number would vary at 200 kHz.

A photon is definitely not a localized em wave or "packet". For ordinary optical frequencies the required electric field strength is 10+ orders of magnitude too high. In addition, em waves don't "stick" together, so any sort of localized packet would disperse fairly quickly.

 

[sophiecentaur]

. The number of photons would be proportional to the magnitude of the radio wave and that number would vary at 200 kHz.

That is definitely not the model of a photon that is generally accepted.

 

[Dickfore]

Actually, radio waves emitted from an antenna are best modeled by a coherent state of the electromagnetic field in which the number of photons is not specified, but obeys a Poisson distribution.

 

[ThomasT]

Hence the spatial and temporal extent of a photon must be considered as zero.

Can't a photon be thought of as a wave front (or sequence thereof, ie., a wave train) whose size is constrained by the channel via which it's transmitted?

 

[YummyFur]

It seems to me that until an agreed definition of what is meant by 'size' when referring to a photon, then the debate is as meaningless as 'does god exist'.

Being a quantum object if we are going to apply a classical concept like size to a photon we really should agree on what we mean by size before saying what this size is.

Can't a photon be thought of as a wave front

that's up to your definition of size. That's what I'm getting at. You have to first contend that a photon is a wave front for your purposes of defining what size is. Then if someone else has an equally valid definition of what size means to them but their definition is different to yours then the two of you would be talking over each other while both being right by your own definitions.

 

[ThomasT]

It seems to me that until an agreed definition of what is meant by 'size' when referring to a photon, then the debate is as meaningless as 'does god exist'.

Being a quantum object if we are going to apply a classical concept like size to a photon we really should agree on what we mean by size before saying what this size is.


that's up to your definition of size. That's what I'm getting at. You have to first contend that a photon is a wave front for your purposes of defining what size is. Then if someone else has an equally valid definition of what size means to them but their definition is different to yours then the two of you would be talking over each other while both being right by your own definitions.

Ok, you've said what I wanted to say but was afraid to say because I was thinking that it might look ignorant. But the way you put it doesn't seem ignorant, it seems like a reasonable consideration. At least that's my current assessment until/unless a qm guru tells us that it's ignorant, and why.

 

[fizzle]

That is definitely not the model of a photon that is generally accepted.

Wel then, what is the correct photon model for a radio wave? Is it one photon or a huge number of them?

 

[sophiecentaur]

Wel then, what is the correct photon model for a radio wave? Is it one photon or a huge number of them?

For a power flux of PWatts, the number of photons would be P/hf (a large number, which gets larger as the frequency gets lower).

Why should the photon model be different for different frequencies of em? The time taken for a particular photon to interact with a suitable charge system (receiver) could involve several periods of oscillation. The number would be determined by the actual system in question (the Q of the resonant circuit, in the case of a radio receiver). Would you say
Your picture of a wave as consisting of a density modulated 'cloud' of photons, with peak density at the extremes of field strength and none at the zero crossings is a bit limiting. If each photon were to interact separately (as with an incoherent beam arriving in a gas of isolated atoms or molecules) you would have a totally opposite situation to what happens when a coherent beam of RF arrives at an antenna and where the photons all 'add up' in phase to produce a sinusoidal output voltage.
Basically I am saying, as has been said many times, in different ways on this thread, that there is just not a suitable model for the photon that is just based on classical ideas. You are stuck with QM and that excludes any simple models. Just like Feynman says in that movie earlier on in the thread. You are doomed to failure if you try.

 

[edguy99]

Actually, radio waves emitted from an antenna are best modeled by a coherent state of the electromagnetic field in which the number of photons is not specified, but obeys a Poisson distribution.

I agree, many waves are not modeled by photons. Water waves, waves on the surface of the sun and radio waves emitted from an antenna (Ultra high frequency as modeled here).

That said, the hydrogen line (21 centimeter line) occurs in that exact range at 1420mhz. Its discovery led to the Hydrogen maser.

Consider the question of how "big" is a photon as it relates to this picture:

The photons are created one by one, are filtered a bit and fly into a microwave cavity that could be some multiple of 21cm big.

It seems pretty clear you need a skinny little thing that has some sort time of variance on a regular basis over time and space to account for the waves that form in the microwave cavity.

This picture suggests that a model of a photon 3fm wide that varies in length from 3fm to 21 cm would complete the picture and you would see some diffraction as the particles entered the cavity and a natural resonance at 1420mhz (21 cm) inside the cavity.

 

[Q-reeus]

...The photons are created one by one, are filtered a bit and fly into a microwave cavity that could be some multiple of 21cm big...

edguy99 - Have a closer read maybe of that Wiki article. It's not photons but atomic hydrogen (red dots in the diagram) that enters the bulb/cavity. Microwave oscillations within the cavity are generated by an external power source in the passive variant, or internally in the active variant (presumably energized via recombination of atomic to molecular hydrogen).

 

[edguy99]

edguy99 - Have a closer read maybe of that Wiki article. It's not photons but atomic hydrogen (red dots in the diagram) that enters the bulb/cavity. Microwave oscillations within the cavity are generated by an external power source in the passive variant, or internally in the active variant (presumably energized via recombination of atomic to molecular hydrogen).

Thank you for the correction, too may wiki searches in too short a time.

 

[Q-reeus]

Thank you for the correction, too may wiki searches in too short a time.

No problem - happens to me all the time - which speaking of is well past my bed time!

 

[fizzle]

Basically I am saying, as has been said many times, in different ways on this thread, that there is just not a suitable model for the photon that is just based on classical ideas. You are stuck with QM and that excludes any simple models. Just like Feynman says in that movie earlier on in the thread. You are doomed to failure if you try.

-deleted reply-

Edit: The thread appears to have been started with the intent to say, yet again, that everyone is "doomed to failure" if they don't accept the status quo. Carry on.

 

[sophiecentaur]

Why should you think that our existing models (e.g. the classical ones or SR) would be sufficient to explain any new thing that is discovered? The Victorians were of that opinion, at the time and I think you'll agree that their ideas were not sufficient.
It may be 'comforting' to have the world presented in old, familiar ways but don't we need to progress?

[edit: I am not saying that QM is sufficient for everything. Of course it's not. My problem is with people who still want stuff to be explained in nice concrete models which pre-date even QM. That's what's doomed to failure.]

 

[fizzle]

Why should you think that our existing models (e.g. the classical ones or SR) would be sufficient to explain any new thing that is discovered?

I don't.

The Victorians were of that opinion, at the time and I think you'll agree that their ideas were not sufficient. It may be 'comforting' to have the world presented in old, familiar ways but don't we need to progress?

Don't be condescending ("comforting"). The Victorians looked through EM-colored glasses, attempting to model everything as EM waves. Today we look through QM-colored glasses, attempting to model everything, no matter how tortured, as QM whatevers. Also, QM is old ... almost 100 years old. It's nothing new.

 

[sophiecentaur]

We're not disagreeing then.

There are many times in the history of Maths where people just had to make these jumps. They couldn't't demand a cuddly way round the square root of minus one. I keep reading demands for the equivalent thing in physics. It has to be 'mechanical'.

 

[fizzle]

We're not disagreeing then.

There are many times in the history of Maths where people just had to make these jumps. They couldn't't demand a cuddly way round the square root of minus one. I keep reading demands for the equivalent thing in physics. It has to be 'mechanical'.

I couldn't disagree more. If something goes from place to place, it has to traverse the intermediate space. If you create a theory that doesn't have that as a fundamental part, then your theory is either tracking fictitious quantities or your theory is simply a higher level calculation shortcut.

 

[sophiecentaur]

it has to traverse the intermediate space.

That is making a huge assumption - based on familiar concepts about space and time. All you can say is that you have observed something leaving and arriving somewhere else. Just like with the two slits experiment, you have no idea how it got there because you need to observe it on its journey to know that and this would involve altering the experiment.

What you say doesn't necessarily 'stand to reason' - it's just a familiar, "comforting" way of thinking about it which mostly produces correct predictions and that's all.

 

[fizzle]

That is making a huge assumption - based on familiar concepts about space and time. All you can say is that you have observed something leaving and arriving somewhere else. Just like with the two slits experiment, you have no idea how it got there because you need to observe it on its journey to know that and this would involve altering the experiment.

When you see the double slit experiment with water waves, do you doubt that the waves went from place to place? No, because the observation tools are high enough quality to see the intermediate steps. You apparently want to revert to action-at-a-distance simply because we haven't constructed adequate measuring devices. Who's making the "huge assumption" now?

What you say doesn't necessarily 'stand to reason' - it's just a familiar, "comforting" way of thinking about it which mostly produces correct predictions and that's all.

My "comfort" with it is no more trivial than your "comfort" with the currently accepted theory.

 

[harrylin]

I couldn't disagree more. If something goes from place to place, it has to traverse the intermediate space. If you create a theory that doesn't have that as a fundamental part, then your theory is either tracking fictitious quantities or your theory is simply a higher level calculation shortcut.

Indeed, modern theories of physics such as QM (and yes, it's getting old now) are merely a mathematical description of observations, lacking a physical model; one may call them "mathematical" theories of physics.